Unconstrained image reconstruction with resolution modelling does not have a unique solution

Positron emission tomography systems have a finite spatial resolution. When the system point spread function (PSF) is taken into account, the unconstrained reconstruction problem does not have a unique solution. As a result, the solution obtained with the maximum likelihood reconstruction algorithm typically suffers from Gibbs artefacts, which can have an adverse effect on tracer uptake quantification in small lesions. To deal with this problem, some assumptions about the undetected image features have to be introduced, either implicitly or explicitly. If one is willing to sacrifice resolution, the improvement of the PSF model can be used to suppress noise and at the same time impose a predefined (suboptimal) spatial resolution, facilitating pooled analysis of multicentre data.